From the top of tower, The angle of elevation of two object on opposite side are alpha and beta respectively . If the distance is p find the height of tower
Answers
Given:from the top of the tower the angle of depression of two objects on the same side of the towers are found to be alpha and beta if the distance between the object is P meter.
To find: show that the height of the tower is given by h of the tower is given by
h=ptanAtanB/tanA-tanB
Solution:
Look the diagram attatched.
CB is tower.
Two objects have angle of depression alpha and beta,from the theory of parallel lines and transversal,angle A and D respectively are alpha and beta,as alternative interior angles are equal.
Let AB= x
Apply trigonometric ratio in ∆ABC
Apply trigonometric ratio in ∆BDC
Put the value of x from eq1
cross multiply
Thus,It has been shown that height of tower is
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